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  <h1>Source code for torch.nn.utils.spectral_norm</h1><div class="highlight"><pre>
<span></span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">Spectral Normalization from https://arxiv.org/abs/1802.05957</span>
<span class="sd">&quot;&quot;&quot;</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch.nn.functional</span> <span class="kn">import</span> <span class="n">normalize</span>


<span class="k">class</span> <span class="nc">SpectralNorm</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
    <span class="c1"># Invariant before and after each forward call:</span>
    <span class="c1">#   u = normalize(W @ v)</span>
    <span class="c1"># NB: At initialization, this invariant is not enforced</span>

    <span class="n">_version</span> <span class="o">=</span> <span class="mi">1</span>
    <span class="c1"># At version 1:</span>
    <span class="c1">#   made  `W` not a buffer,</span>
    <span class="c1">#   added `v` as a buffer, and</span>
    <span class="c1">#   made eval mode use `W = u @ W_orig @ v` rather than the stored `W`.</span>

    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;weight&#39;</span><span class="p">,</span> <span class="n">n_power_iterations</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">dim</span> <span class="o">=</span> <span class="n">dim</span>
        <span class="k">if</span> <span class="n">n_power_iterations</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;Expected n_power_iterations to be positive, but &#39;</span>
                             <span class="s1">&#39;got n_power_iterations=</span><span class="si">{}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">n_power_iterations</span><span class="p">))</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">n_power_iterations</span> <span class="o">=</span> <span class="n">n_power_iterations</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span>

    <span class="k">def</span> <span class="nf">reshape_weight_to_matrix</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">weight</span><span class="p">):</span>
        <span class="n">weight_mat</span> <span class="o">=</span> <span class="n">weight</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">dim</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
            <span class="c1"># permute dim to front</span>
            <span class="n">weight_mat</span> <span class="o">=</span> <span class="n">weight_mat</span><span class="o">.</span><span class="n">permute</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dim</span><span class="p">,</span>
                                            <span class="o">*</span><span class="p">[</span><span class="n">d</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">weight_mat</span><span class="o">.</span><span class="n">dim</span><span class="p">())</span> <span class="k">if</span> <span class="n">d</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
        <span class="n">height</span> <span class="o">=</span> <span class="n">weight_mat</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">weight_mat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">height</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">compute_weight</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">module</span><span class="p">,</span> <span class="n">do_power_iteration</span><span class="p">):</span>
        <span class="c1"># NB: If `do_power_iteration` is set, the `u` and `v` vectors are</span>
        <span class="c1">#     updated in power iteration **in-place**. This is very important</span>
        <span class="c1">#     because in `DataParallel` forward, the vectors (being buffers) are</span>
        <span class="c1">#     broadcast from the parallelized module to each module replica,</span>
        <span class="c1">#     which is a new module object created on the fly. And each replica</span>
        <span class="c1">#     runs its own spectral norm power iteration. So simply assigning</span>
        <span class="c1">#     the updated vectors to the module this function runs on will cause</span>
        <span class="c1">#     the update to be lost forever. And the next time the parallelized</span>
        <span class="c1">#     module is replicated, the same randomly initialized vectors are</span>
        <span class="c1">#     broadcast and used!</span>
        <span class="c1">#</span>
        <span class="c1">#     Therefore, to make the change propagate back, we rely on two</span>
        <span class="c1">#     important behaviors (also enforced via tests):</span>
        <span class="c1">#       1. `DataParallel` doesn&#39;t clone storage if the broadcast tensor</span>
        <span class="c1">#          is already on correct device; and it makes sure that the</span>
        <span class="c1">#          parallelized module is already on `device[0]`.</span>
        <span class="c1">#       2. If the out tensor in `out=` kwarg has correct shape, it will</span>
        <span class="c1">#          just fill in the values.</span>
        <span class="c1">#     Therefore, since the same power iteration is performed on all</span>
        <span class="c1">#     devices, simply updating the tensors in-place will make sure that</span>
        <span class="c1">#     the module replica on `device[0]` will update the _u vector on the</span>
        <span class="c1">#     parallized module (by shared storage).</span>
        <span class="c1">#</span>
        <span class="c1">#    However, after we update `u` and `v` in-place, we need to **clone**</span>
        <span class="c1">#    them before using them to normalize the weight. This is to support</span>
        <span class="c1">#    backproping through two forward passes, e.g., the common pattern in</span>
        <span class="c1">#    GAN training: loss = D(real) - D(fake). Otherwise, engine will</span>
        <span class="c1">#    complain that variables needed to do backward for the first forward</span>
        <span class="c1">#    (i.e., the `u` and `v` vectors) are changed in the second forward.</span>
        <span class="n">weight</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;_orig&#39;</span><span class="p">)</span>
        <span class="n">u</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;_u&#39;</span><span class="p">)</span>
        <span class="n">v</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;_v&#39;</span><span class="p">)</span>
        <span class="n">weight_mat</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">reshape_weight_to_matrix</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span>

        <span class="k">if</span> <span class="n">do_power_iteration</span><span class="p">:</span>
            <span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
                <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_power_iterations</span><span class="p">):</span>
                    <span class="c1"># Spectral norm of weight equals to `u^T W v`, where `u` and `v`</span>
                    <span class="c1"># are the first left and right singular vectors.</span>
                    <span class="c1"># This power iteration produces approximations of `u` and `v`.</span>
                    <span class="n">v</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">mv</span><span class="p">(</span><span class="n">weight_mat</span><span class="o">.</span><span class="n">t</span><span class="p">(),</span> <span class="n">u</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">v</span><span class="p">)</span>
                    <span class="n">u</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">mv</span><span class="p">(</span><span class="n">weight_mat</span><span class="p">,</span> <span class="n">v</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">u</span><span class="p">)</span>
                <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_power_iterations</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
                    <span class="c1"># See above on why we need to clone</span>
                    <span class="n">u</span> <span class="o">=</span> <span class="n">u</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
                    <span class="n">v</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>

        <span class="n">sigma</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">mv</span><span class="p">(</span><span class="n">weight_mat</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
        <span class="n">weight</span> <span class="o">=</span> <span class="n">weight</span> <span class="o">/</span> <span class="n">sigma</span>
        <span class="k">return</span> <span class="n">weight</span>

    <span class="k">def</span> <span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">module</span><span class="p">):</span>
        <span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
            <span class="n">weight</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">compute_weight</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">do_power_iteration</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
        <span class="nb">delattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
        <span class="nb">delattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;_u&#39;</span><span class="p">)</span>
        <span class="nb">delattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;_v&#39;</span><span class="p">)</span>
        <span class="nb">delattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;_orig&#39;</span><span class="p">)</span>
        <span class="n">module</span><span class="o">.</span><span class="n">register_parameter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">(</span><span class="n">weight</span><span class="o">.</span><span class="n">detach</span><span class="p">()))</span>

    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">module</span><span class="p">,</span> <span class="n">inputs</span><span class="p">):</span>
        <span class="nb">setattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">compute_weight</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">do_power_iteration</span><span class="o">=</span><span class="n">module</span><span class="o">.</span><span class="n">training</span><span class="p">))</span>

    <span class="k">def</span> <span class="nf">_solve_v_and_rescale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">weight_mat</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">target_sigma</span><span class="p">):</span>
        <span class="c1"># Tries to returns a vector `v` s.t. `u = normalize(W @ v)`</span>
        <span class="c1"># (the invariant at top of this class) and `u @ W @ v = sigma`.</span>
        <span class="c1"># This uses pinverse in case W^T W is not invertible.</span>
        <span class="n">v</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">chain_matmul</span><span class="p">(</span><span class="n">weight_mat</span><span class="o">.</span><span class="n">t</span><span class="p">()</span><span class="o">.</span><span class="n">mm</span><span class="p">(</span><span class="n">weight_mat</span><span class="p">)</span><span class="o">.</span><span class="n">pinverse</span><span class="p">(),</span> <span class="n">weight_mat</span><span class="o">.</span><span class="n">t</span><span class="p">(),</span> <span class="n">u</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">v</span><span class="o">.</span><span class="n">mul_</span><span class="p">(</span><span class="n">target_sigma</span> <span class="o">/</span> <span class="n">torch</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">mv</span><span class="p">(</span><span class="n">weight_mat</span><span class="p">,</span> <span class="n">v</span><span class="p">)))</span>

    <span class="nd">@staticmethod</span>
    <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">n_power_iterations</span><span class="p">,</span> <span class="n">dim</span><span class="p">,</span> <span class="n">eps</span><span class="p">):</span>
        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">hook</span> <span class="ow">in</span> <span class="n">module</span><span class="o">.</span><span class="n">_forward_pre_hooks</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">hook</span><span class="p">,</span> <span class="n">SpectralNorm</span><span class="p">)</span> <span class="ow">and</span> <span class="n">hook</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="n">name</span><span class="p">:</span>
                <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Cannot register two spectral_norm hooks on &quot;</span>
                                   <span class="s2">&quot;the same parameter </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">name</span><span class="p">))</span>

        <span class="n">fn</span> <span class="o">=</span> <span class="n">SpectralNorm</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">n_power_iterations</span><span class="p">,</span> <span class="n">dim</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
        <span class="n">weight</span> <span class="o">=</span> <span class="n">module</span><span class="o">.</span><span class="n">_parameters</span><span class="p">[</span><span class="n">name</span><span class="p">]</span>

        <span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
            <span class="n">weight_mat</span> <span class="o">=</span> <span class="n">fn</span><span class="o">.</span><span class="n">reshape_weight_to_matrix</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span>

            <span class="n">h</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">weight_mat</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
            <span class="c1"># randomly initialize `u` and `v`</span>
            <span class="n">u</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">weight</span><span class="o">.</span><span class="n">new_empty</span><span class="p">(</span><span class="n">h</span><span class="p">)</span><span class="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="n">fn</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span>
            <span class="n">v</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">weight</span><span class="o">.</span><span class="n">new_empty</span><span class="p">(</span><span class="n">w</span><span class="p">)</span><span class="o">.</span><span class="n">normal_</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="n">fn</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span>

        <span class="nb">delattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">fn</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
        <span class="n">module</span><span class="o">.</span><span class="n">register_parameter</span><span class="p">(</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s2">&quot;_orig&quot;</span><span class="p">,</span> <span class="n">weight</span><span class="p">)</span>
        <span class="c1"># We still need to assign weight back as fn.name because all sorts of</span>
        <span class="c1"># things may assume that it exists, e.g., when initializing weights.</span>
        <span class="c1"># However, we can&#39;t directly assign as it could be an nn.Parameter and</span>
        <span class="c1"># gets added as a parameter. Instead, we register weight.data as a plain</span>
        <span class="c1"># attribute.</span>
        <span class="nb">setattr</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">fn</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="n">weight</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
        <span class="n">module</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s2">&quot;_u&quot;</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
        <span class="n">module</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s2">&quot;_v&quot;</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>

        <span class="n">module</span><span class="o">.</span><span class="n">register_forward_pre_hook</span><span class="p">(</span><span class="n">fn</span><span class="p">)</span>
        <span class="n">module</span><span class="o">.</span><span class="n">_register_state_dict_hook</span><span class="p">(</span><span class="n">SpectralNormStateDictHook</span><span class="p">(</span><span class="n">fn</span><span class="p">))</span>
        <span class="n">module</span><span class="o">.</span><span class="n">_register_load_state_dict_pre_hook</span><span class="p">(</span><span class="n">SpectralNormLoadStateDictPreHook</span><span class="p">(</span><span class="n">fn</span><span class="p">))</span>
        <span class="k">return</span> <span class="n">fn</span>


<span class="c1"># This is a top level class because Py2 pickle doesn&#39;t like inner class nor an</span>
<span class="c1"># instancemethod.</span>
<span class="k">class</span> <span class="nc">SpectralNormLoadStateDictPreHook</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
    <span class="c1"># See docstring of SpectralNorm._version on the changes to spectral_norm.</span>
    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">fn</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">fn</span> <span class="o">=</span> <span class="n">fn</span>

    <span class="c1"># For state_dict with version None, (assuming that it has gone through at</span>
    <span class="c1"># least one training forward), we have</span>
    <span class="c1">#</span>
    <span class="c1">#    u = normalize(W_orig @ v)</span>
    <span class="c1">#    W = W_orig / sigma, where sigma = u @ W_orig @ v</span>
    <span class="c1">#</span>
    <span class="c1"># To compute `v`, we solve `W_orig @ x = u`, and let</span>
    <span class="c1">#    v = x / (u @ W_orig @ x) * (W / W_orig).</span>
    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state_dict</span><span class="p">,</span> <span class="n">prefix</span><span class="p">,</span> <span class="n">local_metadata</span><span class="p">,</span> <span class="n">strict</span><span class="p">,</span>
                 <span class="n">missing_keys</span><span class="p">,</span> <span class="n">unexpected_keys</span><span class="p">,</span> <span class="n">error_msgs</span><span class="p">):</span>
        <span class="n">fn</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fn</span>
        <span class="n">version</span> <span class="o">=</span> <span class="n">local_metadata</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;spectral_norm&#39;</span><span class="p">,</span> <span class="p">{})</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;.version&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">version</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">version</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span>
            <span class="n">weight_key</span> <span class="o">=</span> <span class="n">prefix</span> <span class="o">+</span> <span class="n">fn</span><span class="o">.</span><span class="n">name</span>
            <span class="k">if</span> <span class="n">version</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">(</span><span class="n">weight_key</span> <span class="o">+</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">state_dict</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="p">(</span><span class="s1">&#39;_orig&#39;</span><span class="p">,</span> <span class="s1">&#39;_u&#39;</span><span class="p">,</span> <span class="s1">&#39;_v&#39;</span><span class="p">))</span> <span class="ow">and</span> \
                    <span class="n">weight_key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">state_dict</span><span class="p">:</span>
                <span class="c1"># Detect if it is the updated state dict and just missing metadata.</span>
                <span class="c1"># This could happen if the users are crafting a state dict themselves,</span>
                <span class="c1"># so we just pretend that this is the newest.</span>
                <span class="k">return</span>
            <span class="n">has_missing_keys</span> <span class="o">=</span> <span class="kc">False</span>
            <span class="k">for</span> <span class="n">suffix</span> <span class="ow">in</span> <span class="p">(</span><span class="s1">&#39;_orig&#39;</span><span class="p">,</span> <span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="s1">&#39;_u&#39;</span><span class="p">):</span>
                <span class="n">key</span> <span class="o">=</span> <span class="n">weight_key</span> <span class="o">+</span> <span class="n">suffix</span>
                <span class="k">if</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">state_dict</span><span class="p">:</span>
                    <span class="n">has_missing_keys</span> <span class="o">=</span> <span class="kc">True</span>
                    <span class="k">if</span> <span class="n">strict</span><span class="p">:</span>
                        <span class="n">missing_keys</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">has_missing_keys</span><span class="p">:</span>
                <span class="k">return</span>
            <span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
                <span class="n">weight_orig</span> <span class="o">=</span> <span class="n">state_dict</span><span class="p">[</span><span class="n">weight_key</span> <span class="o">+</span> <span class="s1">&#39;_orig&#39;</span><span class="p">]</span>
                <span class="n">weight</span> <span class="o">=</span> <span class="n">state_dict</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">weight_key</span><span class="p">)</span>
                <span class="n">sigma</span> <span class="o">=</span> <span class="p">(</span><span class="n">weight_orig</span> <span class="o">/</span> <span class="n">weight</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
                <span class="n">weight_mat</span> <span class="o">=</span> <span class="n">fn</span><span class="o">.</span><span class="n">reshape_weight_to_matrix</span><span class="p">(</span><span class="n">weight_orig</span><span class="p">)</span>
                <span class="n">u</span> <span class="o">=</span> <span class="n">state_dict</span><span class="p">[</span><span class="n">weight_key</span> <span class="o">+</span> <span class="s1">&#39;_u&#39;</span><span class="p">]</span>
                <span class="n">v</span> <span class="o">=</span> <span class="n">fn</span><span class="o">.</span><span class="n">_solve_v_and_rescale</span><span class="p">(</span><span class="n">weight_mat</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
                <span class="n">state_dict</span><span class="p">[</span><span class="n">weight_key</span> <span class="o">+</span> <span class="s1">&#39;_v&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>


<span class="c1"># This is a top level class because Py2 pickle doesn&#39;t like inner class nor an</span>
<span class="c1"># instancemethod.</span>
<span class="k">class</span> <span class="nc">SpectralNormStateDictHook</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
    <span class="c1"># See docstring of SpectralNorm._version on the changes to spectral_norm.</span>
    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">fn</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">fn</span> <span class="o">=</span> <span class="n">fn</span>

    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">module</span><span class="p">,</span> <span class="n">state_dict</span><span class="p">,</span> <span class="n">prefix</span><span class="p">,</span> <span class="n">local_metadata</span><span class="p">):</span>
        <span class="k">if</span> <span class="s1">&#39;spectral_norm&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">local_metadata</span><span class="p">:</span>
            <span class="n">local_metadata</span><span class="p">[</span><span class="s1">&#39;spectral_norm&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">{}</span>
        <span class="n">key</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;.version&#39;</span>
        <span class="k">if</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">local_metadata</span><span class="p">[</span><span class="s1">&#39;spectral_norm&#39;</span><span class="p">]:</span>
            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Unexpected key in metadata[&#39;spectral_norm&#39;]: </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">key</span><span class="p">))</span>
        <span class="n">local_metadata</span><span class="p">[</span><span class="s1">&#39;spectral_norm&#39;</span><span class="p">][</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fn</span><span class="o">.</span><span class="n">_version</span>


<div class="viewcode-block" id="spectral_norm"><a class="viewcode-back" href="../../../../nn.html#torch.nn.utils.spectral_norm">[docs]</a><span class="k">def</span> <span class="nf">spectral_norm</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;weight&#39;</span><span class="p">,</span> <span class="n">n_power_iterations</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Applies spectral normalization to a parameter in the given module.</span>

<span class="sd">    .. math::</span>
<span class="sd">        \mathbf{W}_{SN} = \dfrac{\mathbf{W}}{\sigma(\mathbf{W})},</span>
<span class="sd">        \sigma(\mathbf{W}) = \max_{\mathbf{h}: \mathbf{h} \ne 0} \dfrac{\|\mathbf{W} \mathbf{h}\|_2}{\|\mathbf{h}\|_2}</span>

<span class="sd">    Spectral normalization stabilizes the training of discriminators (critics)</span>
<span class="sd">    in Generative Adversarial Networks (GANs) by rescaling the weight tensor</span>
<span class="sd">    with spectral norm :math:`\sigma` of the weight matrix calculated using</span>
<span class="sd">    power iteration method. If the dimension of the weight tensor is greater</span>
<span class="sd">    than 2, it is reshaped to 2D in power iteration method to get spectral</span>
<span class="sd">    norm. This is implemented via a hook that calculates spectral norm and</span>
<span class="sd">    rescales weight before every :meth:`~Module.forward` call.</span>

<span class="sd">    See `Spectral Normalization for Generative Adversarial Networks`_ .</span>

<span class="sd">    .. _`Spectral Normalization for Generative Adversarial Networks`: https://arxiv.org/abs/1802.05957</span>

<span class="sd">    Args:</span>
<span class="sd">        module (nn.Module): containing module</span>
<span class="sd">        name (str, optional): name of weight parameter</span>
<span class="sd">        n_power_iterations (int, optional): number of power iterations to</span>
<span class="sd">            calculate spectral norm</span>
<span class="sd">        eps (float, optional): epsilon for numerical stability in</span>
<span class="sd">            calculating norms</span>
<span class="sd">        dim (int, optional): dimension corresponding to number of outputs,</span>
<span class="sd">            the default is ``0``, except for modules that are instances of</span>
<span class="sd">            ConvTranspose{1,2,3}d, when it is ``1``</span>

<span class="sd">    Returns:</span>
<span class="sd">        The original module with the spectral norm hook</span>

<span class="sd">    Example::</span>

<span class="sd">        &gt;&gt;&gt; m = spectral_norm(nn.Linear(20, 40))</span>
<span class="sd">        &gt;&gt;&gt; m</span>
<span class="sd">        Linear(in_features=20, out_features=40, bias=True)</span>
<span class="sd">        &gt;&gt;&gt; m.weight_u.size()</span>
<span class="sd">        torch.Size([40])</span>

<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">dim</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">ConvTranspose1d</span><span class="p">,</span>
                               <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">ConvTranspose2d</span><span class="p">,</span>
                               <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">ConvTranspose3d</span><span class="p">)):</span>
            <span class="n">dim</span> <span class="o">=</span> <span class="mi">1</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">dim</span> <span class="o">=</span> <span class="mi">0</span>
    <span class="n">SpectralNorm</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">n_power_iterations</span><span class="p">,</span> <span class="n">dim</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">module</span></div>


<div class="viewcode-block" id="remove_spectral_norm"><a class="viewcode-back" href="../../../../nn.html#torch.nn.utils.remove_spectral_norm">[docs]</a><span class="k">def</span> <span class="nf">remove_spectral_norm</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;weight&#39;</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Removes the spectral normalization reparameterization from a module.</span>

<span class="sd">    Args:</span>
<span class="sd">        module (Module): containing module</span>
<span class="sd">        name (str, optional): name of weight parameter</span>

<span class="sd">    Example:</span>
<span class="sd">        &gt;&gt;&gt; m = spectral_norm(nn.Linear(40, 10))</span>
<span class="sd">        &gt;&gt;&gt; remove_spectral_norm(m)</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">hook</span> <span class="ow">in</span> <span class="n">module</span><span class="o">.</span><span class="n">_forward_pre_hooks</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">hook</span><span class="p">,</span> <span class="n">SpectralNorm</span><span class="p">)</span> <span class="ow">and</span> <span class="n">hook</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="n">name</span><span class="p">:</span>
            <span class="n">hook</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">module</span><span class="p">)</span>
            <span class="k">del</span> <span class="n">module</span><span class="o">.</span><span class="n">_forward_pre_hooks</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
            <span class="k">break</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;spectral_norm of &#39;</span><span class="si">{}</span><span class="s2">&#39; not found in </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
            <span class="n">name</span><span class="p">,</span> <span class="n">module</span><span class="p">))</span>

    <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">hook</span> <span class="ow">in</span> <span class="n">module</span><span class="o">.</span><span class="n">_state_dict_hooks</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">hook</span><span class="p">,</span> <span class="n">SpectralNormStateDictHook</span><span class="p">)</span> <span class="ow">and</span> <span class="n">hook</span><span class="o">.</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="n">name</span><span class="p">:</span>
            <span class="k">del</span> <span class="n">module</span><span class="o">.</span><span class="n">_state_dict_hooks</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
            <span class="k">break</span>

    <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">hook</span> <span class="ow">in</span> <span class="n">module</span><span class="o">.</span><span class="n">_load_state_dict_pre_hooks</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">hook</span><span class="p">,</span> <span class="n">SpectralNormLoadStateDictPreHook</span><span class="p">)</span> <span class="ow">and</span> <span class="n">hook</span><span class="o">.</span><span class="n">fn</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="n">name</span><span class="p">:</span>
            <span class="k">del</span> <span class="n">module</span><span class="o">.</span><span class="n">_load_state_dict_pre_hooks</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
            <span class="k">break</span>

    <span class="k">return</span> <span class="n">module</span></div>
</pre></div>

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